Issue with iPhone 5s

I have a iPhone 5s and I was using it and I noticed it was slow and lagging and then all of a sudden it shut down, went completely black, even with the battery at 35% and when I tried to turn it back on, it was unresponsive. So I decided to plug it in and it just stayed on the red power bar icon and when I would unplug the device, it would shut down automatically and would be unresponsive until it was plugged in again. I tried to hard restart it and it didn't work, it would only cause the device to go from the power bar icon, to the apple logo and then right back to the power bar icon. When I tried to restore the device to factory settings via itunes, it would go up until extracting the software was finished and then the device screen would go blank and then right back to the power bar icon, and with repeated attempts, I only garnered the same thing. Also, when it was plugged in and on iTunes, some times the serial number would come up and other times it would be appear as "n/a"

Is there anything I can do to fix this issue, and do any of you guys know what the problem could possibly be?

iPhone 5s, iOS 9.0.2